Can someone help assist me on this Honors Algebra 2 Problem? Challenge Problems #6. The distance from a point on the curve y=√x to the point (2,0) is equal to 2 at what points on the curve? (Hint: Draw a picture.)

 (0, 0) & (3, √3)

Step-by-step explanation:

Since we need a distance of 2, I graphed y = √x and then drew a circle at center (2, 0) and radius of 2 to see where they intersect.

The coordinates of intersection can be determined by solving a system of equations.

Equation 1: y = √x

Equation 2: (x - 2)² + y² = 2²

I will use the Substitution method with Equation 2 to solve for x:

(x - 2)² + (√x)² = 2²        substituted y with √x

x² - 4x + 4 + x = 4           expanded binomial

x² - 3x + 4 = 4                 added like terms

x² - 3x = 0                       subtracted 4 from both sides

x(x - 3) = 0                       factored

x = 0     x - 3 = 0             applied Zero Product Property

            x = 3

Next, solve for y using Equation 1:

x = 0:    y = √0 = 0

x = 3:    y = √3

Coordinates of intersection are: (0, 0) & (3, √3)

24

step-by-step explanation:

the graph shows 30% of students walk. 80 students were questioned, so the number that said they walk is

30% × 80 = 0.30 × 80 = 24